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题目: Computational Conformal Geometry

授课教师：顾险峰教授（纽约州立大学石溪分校)

雷娜教授（大连理工大学软件学院）

摘要：Computational Conformal Geometry is an emerging interdisciplinary field combing mathematics and computer science. In mathematics, conformal geometry is the intersection among complex analysis, differential geometry, algebraic topology, Riemann surface theory and partial differential equation. In computer science, it has been widely applied for many fields, such as computer graphics, computer vision, digital geometry processing, geometric modeling, networking, scientific computing and medical imaging.

This course will cover fundamental mathematics theories in conformal geometry, including homotopy theory and homology theory in algebraic topology; Hodge theory, exterior calculus, De Rham cohomology; surface differential geometry; harmonic mapping theory; Riemann surface theory; Teichmuller quasi-conformal geometry; elliptic partial differential equation and surface Ricci flow. If time allows, we will cover convex geometry, optimal mass transportation theory.

The course also cover fundamental algorithms in computational topoplogy, computational geometry and digitial geometry processing, including algorithms for homotopy group, homology/cohomology group, Hodge decomposition, holomorphic differential forms, conformal structure, conformal module, conformal mapping, quasi-conformal mapping, harmonic maps, Teichmuller map, discrete surface Ricci flow, discrete mass transportation and so on.

Prerequisite:                                        

The course only requires linear algebra and multi-variable calculus. All students from pure mathematics, applied mathematics, and engineering departments are welcomed. Programming skills are preferred but not required.

Reference:

X. Gu and S.-T. Yau, “Computational Conformal Geometry”, Internation Press and High Education Press China

W. Zeng and X. Gu, “Ricci Flow for Shape Analysis and Surface Registration”, Springer

时间：

第一次课：10月20日、22日下午1:30-4:30

之后隔周周末下午1:30-4:30

地点：首都师大北二区教学楼132教室

欢迎全体师生积极参加！